Actinyl(VI, V) (An = U, Np and Pu) complexes of the recently reported hybrid macrocycle, cyclo[1]furan[1]pyridine[4]pyrrole (denoted as H4L), have been studied using density functional theory in combination with the small-core scalar-relativistic effective core potentials and corresponding (14s13p10d8f6g)/[ 10s9p5d4f3g] basis sets in the segmented contraction scheme. On the basis of our calculations, the pyrrole nitrogen atoms that possess the shortest An-L bonds and strongest basicity are the main donor atoms that contribute to the formation of actinyl(VI, V) complexes. The natural population analysis (NPA) suggests higher ligand-to-actinyl charge transfer in the actinyl(VI) complexes than in their actinyl(V) analogues, which account for the higher decomposition energies of the former. A significant actinide-to-ligand spin density delocalization in the uranyl(V) and neptunyl(V) complexes was observed owing to the redistribution of spin density caused by complexation. A thermodynamic analysis indicates that the formation of the actinyl(VI, V) complexes are exothermic reactions in CH2Cl2 solvent, where the uranyl cations show the highest selectivity. In aqueous solution containing chloride ions, for complexing with macrocycle H4L, the plutonyl(VI) and uranyl(V) cations possess the highest selectivity among actinyl(VI) and (V) cations, respectively. This work can shed light on the design of macrocycle complexes for actinide recognition and extraction in the future.